FrOsT: Enabling the Next Generation of Normal-Mode Seismology

Despite the increasing feasibility of fully-numerical simulation of wave propagation, normal mode seismology continues to play an important role: it enables the rapid calculation of exact synthetic seismograms and sensitivity kernels in 1D earth models, and permits both approximate and exact calculations using 3D models. For many day-to-day applications, the improved accuracy of fully-numerical simulations may not justify their computational costs; for other applications -- such as sampling-based approaches to solving inverse problems -- the efficiency of normal mode methods remains essential. Furthermore, observations of free oscillations provide important constraints on long wavelength Earth structure and dynamics.

At present, it is difficult to compute normal modes at frequencies higher than around 100 mHz, due to limitations in software available for these calculations. In order to remove this constraint (among others), and to provide the community with up-to-date software to compute normal mode synthetics in 1D and 3D models, we announce the development of the Free Oscillation Toolkit (FrOsT). In particular, we present new codes for calculating eigenfrequencies and eigenfunctions in arbitrary 1D earth models, and for generating synthetic seismograms using mode summation. We also outline planned software to compute exact synthetic seismograms in 3D models, using mode coupling theory. All codes will be released on an open-source basis in due course.

Our eigenfunction calculations rely on improved radial integration and mode-counting techniques, enabling stable calculations at high frequencies. For mode summation, we adopt the framework of generalised spherical harmonics, with a new algorithm for their efficient calculation. This formalism enables straightforward calculation of strain and rotation fields, in addition to displacement, and the use of higher-order moment tensors. Source parameter sensitivity kernels may also be readily obtained.